Help! Husband wants to store small squares in the kicker wagon

Hi, we have a large three sided hay shed where we stack and store 300 small square bales for two horses. My husband wants to buy two hay wagons, drive them into the shed and grab the bales out of them during the year. His plan is to stack the other 100 or so between the shed and barn.

Will this ruin the hay quality? It will definitely mess with the bale shape, right?, making them a mess to grab? He thinks this is the answer to our stacking problems. I think we should stack them but can't say why. Who is right? Thanks!

Help! Husband wants to store small squares in the kicker wagon